William Tell is said to have shot an apple off his son’s head with an arrow. If the arrow was shot with an initial speed of 50.0 m/s and the boy was 26.0 m away, at what launch angle above the horizontal did Bill aim the arrow? (Assume that the arrow and apple are initially at the same height above the ground. Hint: sin2θ = 2sinθcosθ)

Question
Asked Sep 14, 2019

William Tell is said to have shot an apple off his son’s head with an arrow. If the arrow was shot with an initial speed of 50.0 m/s and the boy was 26.0 m away, at what launch angle above the horizontal did Bill aim the arrow? (Assume that the arrow and apple are initially at the same height above the ground. Hint: sin2θ = 2sinθcosθ)

check_circleExpert Solution
Step 1

Given information:

The apple and the arrow are at the same height before launch.

The initial speed of the arrow (u) = 50 m/s

Distance between the apple and the arrow (R) = 26 m.

Angle of launch (θ) =?

Step 2

We can say that the distance travelled by the arrow launched with an angle (θ) is given by:

R = ucosθ × (time of flight(T))

But “T” for a projectile is given from second equation of motion as follows:

usineT
Since at the end of flight the vertical displacement of the arrow is "Zero" put s 0
We get
2usine
T
g
Substitute this in the equation of "R" we get:
u2 sin20
R
g
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usineT Since at the end of flight the vertical displacement of the arrow is "Zero" put s 0 We get 2usine T g Substitute this in the equation of "R" we get: u2 sin20 R g

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Step 3

Calculation:

For the arrow to hit the apple the condition is R = 26 m, hen...

26= (502)sin20
9.81
0 2.920
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26= (502)sin20 9.81 0 2.920

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